Evidence of cognition in aneural cells is well-establish in the literature. This paper extends the exploration of the mechanisms of cognition by considering whether or not aneural cells may be capable of irrational cognition, making associations based on coincidental similarities and circumstantial factors. If aneural cells do harness such semiosic qualities, as with higher-level creativity, this might be how they are able to overcome old algorithms and invent tools for new situations. I will look at three examples of irrational learning in aneural systems in terms of semiotics: (1) generalisation in the immune system, based on viral molecular mimicry, whereby immune cells attack the self, which seems to be an overgeneralisation of an icon sign based on mere similarity, not identity, (2) the classical conditioning of pea plants to trope toward wind as a sign of light, which seems to be an association of an index sign based on mere temporal proximity, and (3) a pharmaceutical intervention to prevent pregnancy, using a conjugate to encrypt self with non-self, which seems to be an example of symbol use. We identify irrational cognition easily when it leads to 'wrong' outcomes, but, if it occurs, it may also lead to favourable outcomes and 'creative' solutions.image Abstract figure legend The mechanisms behind three examples of 'irrational' semiosis discussed in this paper can be described using terms from semiotics. First, in the case of molecular mimicry, the immune system misrecognises self as an icon of non-self, based on a similarity between human and virus proteins. Second, in a classical conditioning experiment, pea plants were trained to grow either away from or toward wind as a sign of, an index of, approaching light. Third, a conjugate acts as an encryption device, conferring an association, as with an arbitrary conventional symbol, between a toxin and human chorionic gonadotropin.image